# Group 30.1 downloaded from the LMFDB on 13 September 2025. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation GPerm is permutation group 
#	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
# Many characteristics of the group are stored as booleans in a record: 
#	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 
# The character table is stored as a record chartbl_n_i where n is the order 
# of the group and i is which group of that order it is. The record is 
# converted to a character table using ConvertToLibraryCharacterTableNC 

 
# Constructions 
GPC := PcGroupCode(493959,30); a := GPC.1; b := GPC.2;
GPerm := Group( (2,3), (4,5,6,7,8), (1,2,3) );
GLZ := Group([[[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, -1]], [[0, 0, 0, -1, 0, 0], [1, 1, 1, 1, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]]]);
GLFp := Group([[[ Z(11)^0, Z(11)^2 ], [ Z(11), Z(11)^0 ]], [[ Z(11)^0, 0*Z(11) ], [ 0*Z(11), Z(11)^5 ]]]);

 
# Booleans 
booleans_30_1 := rec( 
Agroup := true,
Zgroup := true,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_30_1:=rec(); 
chartbl_30_1.IsFinite:= true; 
chartbl_30_1.UnderlyingCharacteristic:= 0; 
chartbl_30_1.UnderlyingGroup:= GPC;
chartbl_30_1.Size:= 30;
chartbl_30_1.InfoText:= "Character table for group 30.1 downloaded from the LMFDB."; 
chartbl_30_1.Identifier:= " C5*S3 "; 
chartbl_30_1.NrConjugacyClasses:= 15; 
chartbl_30_1.ConjugacyClasses:= [<identity> of ..., f1, f2^2*f3, f3^2, f3^3, f3^4, f3, f1*f3, f1*f2^2, f1*f3^3, f1*f2, f2, f2*f3, f2^2, f2^2*f3^2];
chartbl_30_1.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];
chartbl_30_1.ComputedPowerMaps:= [ , [1, 1, 3, 6, 7, 5, 4, 4, 5, 7, 6, 14, 15, 13, 12], [1, 2, 1, 7, 6, 4, 5, 10, 11, 9, 8, 7, 6, 4, 5], [1, 2, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]];
chartbl_30_1.SizesCentralizers:= [30, 10, 15, 30, 30, 30, 30, 10, 10, 10, 10, 15, 15, 15, 15];
chartbl_30_1.ClassNames:= ["1A", "2A", "3A", "5A1", "5A-1", "5A2", "5A-2", "10A1", "10A-1", "10A3", "10A-3", "15A1", "15A-1", "15A2", "15A-2"];
chartbl_30_1.OrderClassRepresentatives:= [1, 2, 3, 5, 5, 5, 5, 10, 10, 10, 10, 15, 15, 15, 15];
chartbl_30_1.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], [1, 1, 1, E(5)^-2, E(5)^-1, E(5), E(5)^2, E(5)^-1, E(5)^2, E(5), E(5)^-2, E(5)^2, E(5)^-2, E(5), E(5)^-1], [1, 1, 1, E(5)^2, E(5), E(5)^-1, E(5)^-2, E(5), E(5)^-2, E(5)^-1, E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5)], [1, 1, 1, E(5)^-1, E(5)^2, E(5)^-2, E(5), E(5)^2, E(5), E(5)^-2, E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5)^2], [1, 1, 1, E(5), E(5)^-2, E(5)^2, E(5)^-1, E(5)^-2, E(5)^-1, E(5)^2, E(5), E(5)^-1, E(5), E(5)^2, E(5)^-2], [1, -1, 1, E(5)^-2, E(5)^-1, E(5), E(5)^2, -1*E(5)^-1, -1*E(5)^2, -1*E(5), -1*E(5)^-2, E(5)^2, E(5)^-2, E(5), E(5)^-1], [1, -1, 1, E(5)^2, E(5), E(5)^-1, E(5)^-2, -1*E(5), -1*E(5)^-2, -1*E(5)^-1, -1*E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5)], [1, -1, 1, E(5)^-1, E(5)^2, E(5)^-2, E(5), -1*E(5)^2, -1*E(5), -1*E(5)^-2, -1*E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5)^2], [1, -1, 1, E(5), E(5)^-2, E(5)^2, E(5)^-1, -1*E(5)^-2, -1*E(5)^-1, -1*E(5)^2, -1*E(5), E(5)^-1, E(5), E(5)^2, E(5)^-2], [2, 0, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1], [2, 0, -1, 2*E(5)^-2, 2*E(5)^-1, 2*E(5), 2*E(5)^2, 0, 0, 0, 0, -1*E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^-1], [2, 0, -1, 2*E(5)^2, 2*E(5), 2*E(5)^-1, 2*E(5)^-2, 0, 0, 0, 0, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-1, -1*E(5)], [2, 0, -1, 2*E(5)^-1, 2*E(5)^2, 2*E(5)^-2, 2*E(5), 0, 0, 0, 0, -1*E(5), -1*E(5)^-1, -1*E(5)^-2, -1*E(5)^2], [2, 0, -1, 2*E(5), 2*E(5)^-2, 2*E(5)^2, 2*E(5)^-1, 0, 0, 0, 0, -1*E(5)^-1, -1*E(5), -1*E(5)^2, -1*E(5)^-2]];
ConvertToLibraryCharacterTableNC(chartbl_30_1);